Details

analyze4.0ms

Algorithm

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
50%	25%	25%	4
50%	12.5%	37.5%	5
50%	6.2%	43.8%	6
50%	3.1%	46.9%	7
50%	1.6%	48.5%	8
50%	0.8%	49.2%	9
50.4%	0.4%	49.2%	10
50.4%	0.2%	49.4%	11
50.4%	0.1%	49.5%	12
50.4%	0%	49.6%	13
50.4%	0%	49.6%	14

sample73.0ms

Algorithm

intervals

Results

58.0ms	180×	body	1280	valid
7.0ms	39×	body	640	valid
2.0ms	20×	body	320	valid
1.0ms	11×	body	160	valid
0.0ms	6×	body	80	valid

simplify107.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (98.0ms)

Iter	Nodes	Cost
0	4748	13
1	4748	13

prune1.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 30.5b

Counts

2 → 1

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(-.f64 (exp.f64 x) 2)
3.9b	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

9×	`*-un-lft-identity_binary64` `add-log-exp_binary64`
4×	`frac-add_binary64` `add-sqr-sqrt_binary64`
3×	`flip3--_binary64` `flip--_binary64`
2×	`sub-neg_binary64` `pow1_binary64` `diff-log_binary64` `distribute-lft-out_binary64` `neg-sub0_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `exp-diff_binary64` `distribute-lft-out--_binary64` `exp-neg_binary64` `sum-log_binary64`
1×	`flip3-+_binary64` `associate-+l+_binary64` `associate-+l-_binary64` `difference-of-squares_binary64` `+-commutative_binary64` `flip-+_binary64`

Counts

2 → 33

Calls

2 calls:

4.0ms	(-.f64 (exp.f64 x) 2)
8.0ms	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))

series37.0ms

Counts

2 → 6

Calls

2 calls:

7.0ms	(-.f64 (exp.f64 x) 2)
31.0ms	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))

simplify91.0ms

Algorithm

egg-herbie

Counts

39 → 39

Iterations

Useful iterations: 0 (77.0ms)

Iter	Nodes	Cost
0	4880	627
1	4880	627

prune41.0ms

Filtered

28 candidates to 39 candidates (-39.3%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	36	3	39
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	37	3	40

Merged error: 0.0b

Counts

40 → 3

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 1/360 (pow.f64 x 6)) (.f64 1/12 (pow.f64 x 4)))
0.0b	(+.f64 (.f64 x x) (+.f64 (.f64 1/360 (pow.f64 x 6)) (*.f64 1/12 (pow.f64 x 4))))
0.1b	(*.f64 1/360 (pow.f64 x 6))
0.1b	(*.f64 1/12 (pow.f64 x 4))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt_binary64`
14×	`associate-r_binary64` `add-exp-log_binary64`
11×	`add-log-exp_binary64`
10×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
8×	`add-cbrt-cube_binary64` `unpow-prod-down_binary64`
6×	`associate-l_binary64` `unswap-sqr_binary64` `prod-exp_binary64`
4×	`pow1_binary64` `sqr-pow_binary64` `sum-log_binary64`
2×	`pow-to-exp_binary64` `flip3-+_binary64` `cbrt-unprod_binary64` `+-commutative_binary64` `flip-+_binary64` `pow-exp_binary64` `*-commutative_binary64`
1×	`associate-+r+_binary64`

Counts

4 → 74

Calls

4 calls:

5.0ms	(+.f64 (.f64 1/360 (pow.f64 x 6)) (.f64 1/12 (pow.f64 x 4)))
8.0ms	(+.f64 (.f64 x x) (+.f64 (.f64 1/360 (pow.f64 x 6)) (*.f64 1/12 (pow.f64 x 4))))
5.0ms	(*.f64 1/360 (pow.f64 x 6))
6.0ms	(*.f64 1/12 (pow.f64 x 4))

series185.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(+.f64 (.f64 1/360 (pow.f64 x 6)) (.f64 1/12 (pow.f64 x 4)))
30.0ms	(+.f64 (.f64 x x) (+.f64 (.f64 1/360 (pow.f64 x 6)) (*.f64 1/12 (pow.f64 x 4))))
32.0ms	(*.f64 1/360 (pow.f64 x 6))
31.0ms	(*.f64 1/12 (pow.f64 x 4))

simplify94.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (75.0ms)

Iter	Nodes	Cost
0	5109	1259

prune69.0ms

Filtered

55 candidates to 86 candidates (-56.4%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	85	1	86
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	85	4	89

Merged error: 0.0b

Counts

89 → 4

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (+.f64 (+.f64 2 (pow.f64 (exp.f64 x) 3)) (.f64 (exp.f64 x) -3)) (.f64 (exp.f64 x) (+.f64 (exp.f64 x) 2)))
0.0b	(*.f64 (exp.f64 x) (+.f64 (exp.f64 x) 2))
0.0b	(pow.f64 (exp.f64 x) 3)
2.9b	(+.f64 (+.f64 2 (pow.f64 (exp.f64 x) 3)) (*.f64 (exp.f64 x) -3))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

14×	`*-un-lft-identity_binary64` `add-sqr-sqrt_binary64`
12×	`add-cube-cbrt_binary64` `add-cbrt-cube_binary64`
9×	`add-log-exp_binary64` `add-exp-log_binary64`
7×	`pow1_binary64`
4×	`flip3-+_binary64` `associate-r_binary64` `associate-*r/_binary64` `pow-pow_binary64` `flip-+_binary64`
3×	`pow-unpow_binary64` `associate-l_binary64` `unpow-prod-down_binary64` `cube-prod_binary64` `associate-/l*_binary64` `times-frac_binary64` `exp-prod_binary64` `sum-log_binary64`
2×	`associate-/l/_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `associate-/r/_binary64` `prod-exp_binary64` `div-exp_binary64`
1×	`pow-to-exp_binary64` `pow-prod-down_binary64` `associate-/r_binary64` `distribute-lft-out_binary64` `associate-+l+_binary64` `sqr-pow_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `unswap-sqr_binary64` `clear-num_binary64` `rem-cube-cbrt_binary64` `frac-2neg_binary64` `div-inv_binary64` `+-commutative_binary64` `pow-exp_binary64` `unpow3_binary64` `-commutative_binary64` `cube-mult_binary64`

Counts

4 → 87

Calls

4 calls:

17.0ms	(/.f64 (+.f64 (+.f64 2 (pow.f64 (exp.f64 x) 3)) (.f64 (exp.f64 x) -3)) (.f64 (exp.f64 x) (+.f64 (exp.f64 x) 2)))
8.0ms	(*.f64 (exp.f64 x) (+.f64 (exp.f64 x) 2))
4.0ms	(pow.f64 (exp.f64 x) 3)
11.0ms	(+.f64 (+.f64 2 (pow.f64 (exp.f64 x) 3)) (*.f64 (exp.f64 x) -3))

series230.0ms

Counts

4 → 12

Calls

4 calls:

139.0ms	(/.f64 (+.f64 (+.f64 2 (pow.f64 (exp.f64 x) 3)) (.f64 (exp.f64 x) -3)) (.f64 (exp.f64 x) (+.f64 (exp.f64 x) 2)))
17.0ms	(*.f64 (exp.f64 x) (+.f64 (exp.f64 x) 2))
23.0ms	(pow.f64 (exp.f64 x) 3)
51.0ms	(+.f64 (+.f64 2 (pow.f64 (exp.f64 x) 3)) (*.f64 (exp.f64 x) -3))

simplify64.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5582	1863

prune90.0ms

Filtered

70 candidates to 99 candidates (-41.4%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	99	0	99
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	99	4	103

Merged error: 0.0b

Counts

103 → 4

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow.f64 (-.f64 (exp.f64 x) 2) 3)
0.0b	(pow.f64 (exp.f64 x) -3)
0.3b	(/.f64 (+.f64 (pow.f64 (-.f64 (exp.f64 x) 2) 3) (pow.f64 (exp.f64 x) -3)) (+.f64 (pow.f64 (exp.f64 x) -2) (*.f64 (-.f64 (exp.f64 x) 2) (-.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x))))))
3.8b	(+.f64 (pow.f64 (-.f64 (exp.f64 x) 2) 3) (pow.f64 (exp.f64 x) -3))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

33×	`*-un-lft-identity_binary64`
23×	`add-sqr-sqrt_binary64`
19×	`add-cube-cbrt_binary64`
12×	`times-frac_binary64`
8×	`unpow-prod-down_binary64`
7×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
6×	`pow-unpow_binary64` `add-log-exp_binary64` `pow1_binary64`
5×	`distribute-lft-out_binary64` `pow-pow_binary64` `cube-prod_binary64`
4×	`associate-/l*_binary64`
3×	`flip3-+_binary64` `associate-/r*_binary64` `flip-+_binary64` `exp-prod_binary64`
2×	`pow-to-exp_binary64` `associate-/l/_binary64` `sqr-pow_binary64` `associate-/r/_binary64` `cube-div_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64` `pow-exp_binary64`
1×	`flip3--_binary64` `cbrt-undiv_binary64` `clear-num_binary64` `rem-cube-cbrt_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `+-commutative_binary64` `flip--_binary64` `unpow3_binary64` `sum-log_binary64` `cube-mult_binary64`

Counts

4 → 96

Calls

4 calls:

8.0ms	(pow.f64 (-.f64 (exp.f64 x) 2) 3)
3.0ms	(pow.f64 (exp.f64 x) -3)
20.0ms	(/.f64 (+.f64 (pow.f64 (-.f64 (exp.f64 x) 2) 3) (pow.f64 (exp.f64 x) -3)) (+.f64 (pow.f64 (exp.f64 x) -2) (*.f64 (-.f64 (exp.f64 x) 2) (-.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x))))))
15.0ms	(+.f64 (pow.f64 (-.f64 (exp.f64 x) 2) 3) (pow.f64 (exp.f64 x) -3))

series700.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(pow.f64 (-.f64 (exp.f64 x) 2) 3)
40.0ms	(pow.f64 (exp.f64 x) -3)
495.0ms	(/.f64 (+.f64 (pow.f64 (-.f64 (exp.f64 x) 2) 3) (pow.f64 (exp.f64 x) -3)) (+.f64 (pow.f64 (exp.f64 x) -2) (*.f64 (-.f64 (exp.f64 x) 2) (-.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x))))))
131.0ms	(+.f64 (pow.f64 (-.f64 (exp.f64 x) 2) 3) (pow.f64 (exp.f64 x) -3))

simplify69.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	6013	3536

prune141.0ms

Filtered

72 candidates to 108 candidates (-50.0%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	107	1	108
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	107	5	112

Merged error: 0b

Counts

112 → 5

regimes15.0ms

Accuracy

0% (0.6b remaining)

Error of 0.7b against oracle of 0.1b and baseline of 0.7b

bsearch0.0ms

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	22
1	17	22

end0.0ms

sample2.3s

Algorithm

intervals

Results

1.9s	5709×	body	1280	valid
228.0ms	1240×	body	640	valid
68.0ms	581×	body	320	valid
28.0ms	310×	body	160	valid
6.0ms	160×	body	80	valid
0.0ms	1×	body	80	invalid

Details

analyze4.0ms

sample73.0ms

simplify107.0ms

prune1.0ms

localize6.0ms

rewrite14.0ms

series37.0ms

simplify91.0ms

prune41.0ms

localize9.0ms

rewrite27.0ms

series185.0ms

simplify94.0ms

prune69.0ms

localize10.0ms

rewrite42.0ms

series230.0ms

simplify64.0ms

prune90.0ms

localize15.0ms

rewrite50.0ms

series700.0ms

simplify69.0ms

prune141.0ms

regimes15.0ms

bsearch0.0ms

simplify3.0ms

end0.0ms

sample2.3s

Profiling